A random variable X follows the exponential distribution if it has the following probability density function (PDF):
Question:
A random variable X follows the exponential distribution if it has the following probability density function (PDF):
f(X) = (1/θ)e-X/θ for X > 0
= 0 elsewhere
where θ > 0 is the parameter of the distribution. Using the ML method, show that the ML estimator of θ is θ̂ = ΣXi /n, where n is the sample size. That is, show that the ML estimator of θ is the sample mean X̅.
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